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Simplifying (y3) + -1(3y2) + 2y + (y3) + -1(3y2) + 2y + 2 = (2y2) + -4y + 2 y3 + -1(3y2) + 2y + (y3) + -1(3y2) + 2y + 2 = (2y2) + -4y + 2 Remove parenthesis around (3y2) y3 + -1 * 3y2 + 2y + (y3) + -1(3y2) + 2y + 2 = (2y2) + -4y + 2 Multiply -1 * 3 y3 + -3y2 + 2y + (y3) + -1(3y2) + 2y + 2 = (2y2) + -4y + 2 y3 + -3y2 + 2y + y3 + -1(3y2) + 2y + 2 = (2y2) + -4y + 2 Remove parenthesis around (3y2) y3 + -3y2 + 2y + y3 + -1 * 3y2 + 2y + 2 = (2y2) + -4y + 2 Multiply -1 * 3 y3 + -3y2 + 2y + y3 + -3y2 + 2y + 2 = (2y2) + -4y + 2 Reorder the terms: 2 + 2y + 2y + -3y2 + -3y2 + y3 + y3 = (2y2) + -4y + 2 Combine like terms: 2y + 2y = 4y 2 + 4y + -3y2 + -3y2 + y3 + y3 = (2y2) + -4y + 2 Combine like terms: -3y2 + -3y2 = -6y2 2 + 4y + -6y2 + y3 + y3 = (2y2) + -4y + 2 Combine like terms: y3 + y3 = 2y3 2 + 4y + -6y2 + 2y3 = (2y2) + -4y + 2 Reorder the terms: 2 + 4y + -6y2 + 2y3 = 2 + -4y + (2y2) Add '-2' to each side of the equation. 2 + 4y + -6y2 + -2 + 2y3 = 2 + -4y + -2 + (2y2) Reorder the terms: 2 + -2 + 4y + -6y2 + 2y3 = 2 + -4y + -2 + (2y2) Combine like terms: 2 + -2 = 0 0 + 4y + -6y2 + 2y3 = 2 + -4y + -2 + (2y2) 4y + -6y2 + 2y3 = 2 + -4y + -2 + (2y2) Reorder the terms: 4y + -6y2 + 2y3 = 2 + -2 + -4y + (2y2) Combine like terms: 2 + -2 = 0 4y + -6y2 + 2y3 = 0 + -4y + (2y2) 4y + -6y2 + 2y3 = -4y + (2y2) Solving 4y + -6y2 + 2y3 = -4y + (2y2) Solving for variable 'y'. Reorder the terms: 4y + 4y + -6y2 + (-2y2) + 2y3 = -4y + (2y2) + 4y + (-2y2) Combine like terms: 4y + 4y = 8y 8y + -6y2 + (-2y2) + 2y3 = -4y + (2y2) + 4y + (-2y2) Combine like terms: -6y2 + (-2y2) = -8y2 8y + -8y2 + 2y3 = -4y + (2y2) + 4y + (-2y2) Reorder the terms: 8y + -8y2 + 2y3 = -4y + 4y + (2y2) + (-2y2) Combine like terms: -4y + 4y = 0 8y + -8y2 + 2y3 = 0 + (2y2) + (-2y2) 8y + -8y2 + 2y3 = (2y2) + (-2y2) Combine like terms: (2y2) + (-2y2) = 0 8y + -8y2 + 2y3 = 0 Factor out the Greatest Common Factor (GCF), '2y'. 2y(4 + -4y + y2) = 0 Factor a trinomial. 2y((2 + -1y)(2 + -1y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0Subproblem 2
Set the factor '(2 + -1y)' equal to zero and attempt to solve: Simplifying 2 + -1y = 0 Solving 2 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1y = 0 + -2 -1y = 0 + -2 Combine like terms: 0 + -2 = -2 -1y = -2 Divide each side by '-1'. y = 2 Simplifying y = 2Subproblem 3
Set the factor '(2 + -1y)' equal to zero and attempt to solve: Simplifying 2 + -1y = 0 Solving 2 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1y = 0 + -2 -1y = 0 + -2 Combine like terms: 0 + -2 = -2 -1y = -2 Divide each side by '-1'. y = 2 Simplifying y = 2Solution
y = {0, 2, 2}
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